Problem: A circle has a sector with area $4\pi$ and central angle $160^\circ$. What is the area of the circle? ${9\pi}$ $\color{#9D38BD}{160^\circ}$ ${4\pi}$
Solution: The ratio between the sector's central angle $\theta$ and $360^\circ$ is equal to the ratio between the sector's area, $A_s$ , and the whole circle's area, $A_c$ $\dfrac{\theta}{360^\circ} = \dfrac{A_s}{A_c}$ $\dfrac{160^\circ}{360^\circ} = 4\pi \div A_c$ $\dfrac{4}{9} = 4\pi \div A_c$ $A_c \times \dfrac{4}{9} = 4\pi$ $A_c = 4\pi \times \dfrac{9}{4}$ $A_c = 9\pi$